Localizations for construction of quantum coset spaces

• Autorzy: Zoran Škoda
• Języki publikacji: EN

Abstrakty

EN

Viewing comodule algebras as the noncommutative analogues of affine varieties with affine group actions, we propose rudiments of a localization approach to nonaffine Hopf algebraic quotients of noncommutative affine varieties corresponding to comodule algebras. After reviewing basic background on noncommutative localizations, we introduce localizations compatible with coactions. Coinvariants of these localized coactions give local information about quotients. We define Zariski locally trivial quantum group algebraic principal and associated bundles. Compatible localizations induce localizations on the categories of Hopf modules. Their interplay with the functor of taking coinvariants and its left adjoint is stressed out. Using the localization approach, we construct a natural class of examples of quantum coset spaces, related to the quantum flag varieties of type A of other authors. Noncommutative Gauss decomposition via quasideterminants reveals a new structure in noncommutative matrix bialgebras. In the quantum case, calculations with quantum minors yield structure theorems.

Kategorie tematyczne

• 58B32: Geometry of quantum groups
• 14L30: Group actions on varieties or schemes (quotients)
• 14A22: Noncommutative algebraic geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 61
• Numer: 1
• Strony: 265-298

Daty

wydano

2003

Twórcy

autor

Zoran Škoda

• Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405, U.S.A.

Identyfikatory

DOI

10.4064/bc61-0-17